Related papers: Time-dependent quantum harmonic oscillator: a cont…
We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from $\hat{H}_0$ to $\hat{H}_1$ in a…
Transition amplitudes between instantaneous eigenstates of quantum two-level system are evaluated analytically on the basis of a new parametrization of its evolution operator, which has recently been proposed to construct exact solutions.…
The dynamics of a periodically driven system whose time evolution is governed by the Schr\"{o}dinger equation with non-Hermitian Hamiltonians can be perfectly stable. This finding was only obtained very recently and will be enhanced by many…
We study the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative $\mathds{R}^{1,1}$ perturbatively to linear order in the noncommutativity $\theta$. We show that the Poisson distribution gets modified,…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
It is a fundamental problem to characterize the nonequilibrium processes. For a slowly moving one-dimensional potential, we explore the quasi adiabatic dynamics of the initial energy eigenstates for a confined quantum system interacting…
Quantum adiabaticity is the evolution of a quantum system that remains close to an instantaneous eigenstate of a time-dependent Hamiltonian. Using Floquet formalism, we derive a rigorous sufficient condition for adiabaticity in closed,…
The effect of a temporal modulation at three times the critical frequency on a Hopf bifurcation is studied in the framework of amplitude equations. We consider a complex Ginzburg-Landau equation with an extra quadratic term, resulting from…
Keeping a quantum system in a given instantaneous eigenstate is a control problem with numerous applications, e.g., in quantum information processing. The problem is even more challenging in the setting of open quantum systems, where…
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process…
The effect of phase space general noncommutativity on producing deformed coherent squeezed states is examined. A two-dimensional noncommutative quantum system supported by a deformed mathematical structure similar to that of Hadamard…
We propose a method to produce fast transitionless dynamics for finite-dimensional quantum systems without requiring additional Hamiltonian components not included in the initial control setup, remaining close to the true adiabatic path at…
We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field, when this field changes adiabatically its sign. We show that after a single magnetic field passage through zero…
We analyze the crossing of a quantum critical point based on exact results for the transverse XY model. In dependence of the change rate of the driving field, the evolution of the ground state is studied while the transverse magnetic field…
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The…
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between non-degenerate instantaneous eigen-energy levels in such a…
We study properties of steady states (states with time-independent density operators) of systems of coupled harmonic oscillators. Formulas are derived showing how adiabatic change of the Hamiltonian transforms one steady state into another.…
Quantum systems subject to time periodic fields of finite amplitude, lambda, have conventionally been handled either by low order perturbation theory, for lambda not too large, or by exact diagonalization within a finite basis of N states.…
In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is…
Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency $\omega_0$, that…